Thank you for visiting Calculate the following tex 10 12 8 3 tex Determine the HCF of 330 and 396 using prime factorization. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Sure! Let's go through the problem step-by-step.
1. Calculate the expression: [tex]\(10 + 12 - (8 - 3)\)[/tex]
First, we solve the operation inside the parentheses:
- [tex]\(8 - 3 = 5\)[/tex]
Next, substitute the result back into the expression:
- [tex]\(10 + 12 - 5\)[/tex]
Finally, perform the addition and subtraction from left to right:
- [tex]\(10 + 12 = 22\)[/tex]
- [tex]\(22 - 5 = 17\)[/tex]
So, the result of the expression is [tex]\(17\)[/tex].
2. Determine the Highest Common Factor (HCF) of 330 and 396 using prime factorization
First, find the prime factors of each number:
- Prime factorization of 330:
- 330 is divisible by 2: [tex]\(330 \div 2 = 165\)[/tex]
- 165 is divisible by 3: [tex]\(165 \div 3 = 55\)[/tex]
- 55 is divisible by 5: [tex]\(55 \div 5 = 11\)[/tex]
- 11 is a prime number
- So, the prime factors of 330 are [tex]\(2, 3, 5, 11\)[/tex].
- Prime factorization of 396:
- 396 is divisible by 2: [tex]\(396 \div 2 = 198\)[/tex]
- 198 is divisible by 2 again: [tex]\(198 \div 2 = 99\)[/tex]
- 99 is divisible by 3: [tex]\(99 \div 3 = 33\)[/tex]
- 33 is divisible by 3 again: [tex]\(33 \div 3 = 11\)[/tex]
- 11 is a prime number
- So, the prime factors of 396 are [tex]\(2, 2, 3, 3, 11\)[/tex].
Now, identify the common prime factors and calculate the HCF:
- Common prime factors: [tex]\(2, 3, 11\)[/tex]
Multiply the common factors together:
- HCF = [tex]\(2 \times 3 \times 11 = 66\)[/tex]
Therefore, the HCF of 330 and 396 is 66.
In conclusion, the solution to the problem is:
- The result of the expression [tex]\(10 + 12 - (8 - 3)\)[/tex] is 17.
- The HCF of 330 and 396 is 66.
1. Calculate the expression: [tex]\(10 + 12 - (8 - 3)\)[/tex]
First, we solve the operation inside the parentheses:
- [tex]\(8 - 3 = 5\)[/tex]
Next, substitute the result back into the expression:
- [tex]\(10 + 12 - 5\)[/tex]
Finally, perform the addition and subtraction from left to right:
- [tex]\(10 + 12 = 22\)[/tex]
- [tex]\(22 - 5 = 17\)[/tex]
So, the result of the expression is [tex]\(17\)[/tex].
2. Determine the Highest Common Factor (HCF) of 330 and 396 using prime factorization
First, find the prime factors of each number:
- Prime factorization of 330:
- 330 is divisible by 2: [tex]\(330 \div 2 = 165\)[/tex]
- 165 is divisible by 3: [tex]\(165 \div 3 = 55\)[/tex]
- 55 is divisible by 5: [tex]\(55 \div 5 = 11\)[/tex]
- 11 is a prime number
- So, the prime factors of 330 are [tex]\(2, 3, 5, 11\)[/tex].
- Prime factorization of 396:
- 396 is divisible by 2: [tex]\(396 \div 2 = 198\)[/tex]
- 198 is divisible by 2 again: [tex]\(198 \div 2 = 99\)[/tex]
- 99 is divisible by 3: [tex]\(99 \div 3 = 33\)[/tex]
- 33 is divisible by 3 again: [tex]\(33 \div 3 = 11\)[/tex]
- 11 is a prime number
- So, the prime factors of 396 are [tex]\(2, 2, 3, 3, 11\)[/tex].
Now, identify the common prime factors and calculate the HCF:
- Common prime factors: [tex]\(2, 3, 11\)[/tex]
Multiply the common factors together:
- HCF = [tex]\(2 \times 3 \times 11 = 66\)[/tex]
Therefore, the HCF of 330 and 396 is 66.
In conclusion, the solution to the problem is:
- The result of the expression [tex]\(10 + 12 - (8 - 3)\)[/tex] is 17.
- The HCF of 330 and 396 is 66.
Thank you for reading the article Calculate the following tex 10 12 8 3 tex Determine the HCF of 330 and 396 using prime factorization. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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